Question

Find the interval in which the following function is increasing or decreasing.
$f\left(x\right)=3x^4-4x^3-12x^2+5$

Answer 1

$f\left(x\right)=3x^4-4x^3-12x^2+5$

$f^{\prime }\left(x\right)=12x^3-12x^2-24x$

$=12x(x^2-x-2)$

$=12x(x+1)(x-2)$

for $f\left(x\right)$ to be increasing $f^{\prime }\left(x\right)>0$

i.e $12x(x+1)(x-2)>0$

$f\left(x\right)$ is increasing in $(-1,0)\cup (2,\infty )$

deceasing in $(-\infty ,-1)\cup (0,2)$